A022646 Expansion of Product_{m>=1} (1 + m*q^m)^18.

1, 18, 189, 1518, 10224, 60552, 324657, 1606050, 7429455, 32458628, 134950419, 537136776, 2056614597, 7604901990, 27248140107, 94861629852, 321652565253, 1064430256536, 3443952349385, 10911585508344, 33900910277472, 103410118026774, 310042892332701, 914572545220908

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=18 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^18:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 2018

Maple

[seq(coeff(series(mul((1+m*q^m)^(18), m=1..100),q,101),q,j),j=0..25)]; # Muniru A Asiru, Feb 18 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^18, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 17 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^18)) \\ G. C. Greubel, Feb 17 2018